STABILITY АND MONOTONICITY OF TIME-DEPENDENT HEAT CONDUCTION PROBLEM SOLUTIONS OBTAINED WITH FINITE-ELEMENT AND FINITE-DIFFERENCE METHODS

A.G. Tsitsin, K.E. Afanasiev
VANT. Ser. Mat. Mod. Fiz. Proc 1991. Вып.3. С. 46-49.

      Increasing finite element and finite-difference scheme accuracy order results in additional restrictions on dimension- less timestep size (similar to Courant criterion) which are due to the solution monotonicity over space. For a one-dimensional heat conduction problem with linear Laplace operator approximation, a range of allowed Courant criterion values ensuring the stability and monotonicity of schemes under question is plotted.